I hear you, Tony, about why you chose to be Non-Denominational. One of my few pet peeves is Denominational-ism. I believe that it is against everything which Jesus prayed for the church in his prayer to the Father as He prepared for the cross and His physical departure in John 17. Romans 14 is also a treatise, I believe, against Denominational-ism. And then we have the Apostle Paul who repudiated any kind of a breaking off from Christ's church and trying to form separate and unique sub-followings or sects such as in 1 Cor 1: 11-13 and 1 Cor 3: 3-4, 21-22 as follows: "For I have been informed concerning you, my brethren, by Chloe’s people, that there are quarrels among you. Now I mean this, that each one of you is saying, “I am of Paul,” and “I of Apollos,” and “I of Cephas,” and “I of Christ.” Has Christ been divided? Paul was not crucified for you, was he? Or were you baptized in the name of Paul? " and "...for you are still worldly. For since there is jealousy and dissension among you, are you not worldly? Are you not walking in the way of man? For when one of you says, “I follow Paul,” and another, “I follow Apollos,” are you not mere men?" and "Therefore, stop boasting in men. All things are yours, whether Paul or Apollos or Cephas or the world or life or death or the present or the future. All of them belong to you, and you belong to Christ, and Christ belongs to God."
Yes, Paul, in the Spirit of Christ, confronted any such breaking down/division of Christ's church. Paul was the great ambassador of Christ to the world, so to speak. He went on at least 3 missionary journeys preaching the Gospel and establishing and maintaining Christ's church, especially to Gentiles. He was probably the first to really see how the division of the church was hurting Christ and the first to try to quench it. Gentile converts struggled with bringing attributes of their past Non-Jewish national or cultural faiths, esp pantheism into their Christian style of worship.
The most effective way to defeat an enemy is to divide and conquer whether by military force or more subtly, from within by causing philosophical, theological, cultural, and such divisions. Satan is our enemy and he knows and uses that strategy very effectively. One very powerful means of this has been to divide Christ's church into sub-groups which have become disconnected and sadly exclusively loyal only to ones of their specific title or name and have forgotten or ignored Jesus' repetitive plea for UNITY in His church as He looked forward in history (Omnipresence) at the division of His church in John 17.
I would think that changing your position label to "Anti-Denomination" is not necessary, Tony. Just because someone wrongly describes themselves as Non-Denominational doesn't that you have to let them boot you out. That is their problem.
One Non-Denominational church which we attended for about 8 yrs identified itself as "Independent Non-Denominational Bible." The "Bible" part referring to the fact that no institution or denomination dictated its doctrine and practices and procedures but rather the Bible, exclusively, and the "Independent" referring to the fact that it was autonomous from any earthly dictated doctrine, practices, procedures, and such..